old hard drive in a new (to me) computer

A couple days ago my cat spilled water on my computer (macbook pro mid 2009) and now it wont turn on. I recently discovered that the battery was not holding any change so I decided to buy a new computer since it was needed anyway. I have a 2012 macbook pro in the mail.

My question is whether I can put the hard drive from the 2009 computer, one i installed myself, into the new computer when it arrives and have all my old files. I couldn't update beyond el capitan and I know the new computer will have high sierra, will this complicate things? I have a time machine with all the files so it wont be a big deal of not, it would just be easier as I plan on putting the old hard drive in anyway.